To calculate radiation fields in the concrete biological shield (CBS) of the VVER-1000 reactor in this work, we have developed and applied the Monte Carlo code Serpent simulation framework based on the variance reduction technique. We have quantified the radial, axial, and azimuthal variation of neutron and gamma-ray fluxes and the absorbed dose rate in the CBS. Using the calculation results, we estimate maximum neutron fluence and maximum absorbed dose in the VVER-1000 CBS over the period of 60 and 80 years of the reactor operation and localize the domains of highest radiation exposure. The obtained results are in good agreement with the available data on the VVER-1000 and other pressurized water reactors. We show that the fluence of neutrons with energy above 0.1 MeV decreases by half at a depth of 4 cm of concrete, and the gamma-ray absorbed dose decreases by 40 % at a depth of 13.5 cm. The outcomes from this research will help to assess the effects of prolonged irradiation of the VVER-1000 CBS, which is required for reliable risk assessment for extended operation of nuclear power plants.